Exponent Rules

In the example shown in the box, the 5 is called the base. The 2 is called the exponent or index or power.
5 to the power of 2 = 5 × 5 = 25

INDEX RULES

Rules

Examples

Expanding

an = a × a × a × ...... × a

35 = 3 × 3 × 3 × 3 × 3 = 243

Multiplying

ax × ay = a(x+y)

36 × 32 = 3(6+2) = 38 = 6561

Dividing

ax ÷ ay = a(x–y)

36 ÷ 32 = 3(6–2) = 34 = 81

Fractional index

a(1/x) = xth root of a

9(1/2) = √9 = 3

Negative index

a –1 =

1

ax

3 –2 =

1

=

1

32

9

Example One - Expanding

Expand 53

Answer:53= 5 × 5 × 5
= 125

Questions

Expand these.
Q1. 55Q2. 106

AnswersA1. 3125
A2. 1 000 000

Maths Fun - Body Bacteria

How many bacteria are on your body NOW? Here are some facts to help you work it out...

There about 5 million bacteria on every centimetre2 of your skin.

An adult has about 2 metres2 (20 000 centimetres2) of skin.

That probably took a minute for you to work out. How many bacteria are on your skin NOW (a minute later)?
Bacteria reproduce by binary fission (splitting in half) every 20 minutes. Therefore, all those bacteria have
reproduced (doubled in number) 3 times in the last minute!